A global model defines a family of curves, rather than just a single curve. Some parameters are shared so a single parameter value applies to all the curves, while other parameters apply to each data individually. For each shared parameter, fit one (global) best-fit value that applies to all the data sets. For each non-shared parameter, fit a separate (local) best-fit value for each data set.
Nonlinear regression finds parameters of a model that make the curve come as close as possible to the data. This is done by minimizing the sum of the squares of the vertical distances between the data points and curve. Global nonlinear regression extends this idea to fitting several data sets at once and minimizes the sum (of all data sets) of sum (of all data points) of squares.
Prism makes it very easy to perform global nonlinear regression. Enter your data on one data table, click analyze, choose nonlinear regression and choose a model. On the Constrain tab of the Nonlinear regression dialog, choose which parameter(s) to share among data sets.